If you bought 1000 points, you'll see 1000CP in both games. If you get a 400 champs points stipend, you'll see 1000CP and 400 Champs Points, when playing champs. If you were to get 600 STO points somehow, when playing STO you'd see 1000CP and 600 STO points).

This isn't actually hooked up in game yet, so the final UI for all that is subject to change, but that's the general idea.